Question

find the compound interest on rupees 5000 for 3 years at 5% also find the simple interest for rupees 5000 for 3 years at 6% find the difference in interest​

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\sf{Principal = Rs. \:5000}\\\sf{Time = 3 \:Years}\\ \sf{Rate = 5\% \: p.a.}\\\sf{Compound \:Interest=?} \end{cases}$

• Calculation of Compound Interest :

$\longrightarrow \tt CI = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t}-1 \bigg] \\ \\\longrightarrow \tt CI = \bigg[5000\bigg(1 + \cancel\dfrac{5}{100} \bigg)^{3}-1 \bigg] \\ \\\longrightarrow \tt CI = \bigg[5000\bigg(1 + \dfrac{1}{20} \bigg)^{3}-1 \bigg] \\ \\\longrightarrow \tt CI = \bigg[5000\bigg(\dfrac{21}{20} \bigg)^{3}-1\bigg] \\ \\\longrightarrow \tt CI = \bigg[5000\bigg(\dfrac{9261}{8000} - 1\bigg)\bigg] \\ \\\longrightarrow \tt CI = \bigg[5000\bigg(\dfrac{9261 - 8000}{8000}\bigg)\bigg] \\ \\\longrightarrow \tt CI = 5\cancel{000} \times \dfrac{1261}{8 \cancel{000}} \\ \\\longrightarrow \tt CI =\dfrac{5 \times 1261}{8} \\ \\\longrightarrow \tt CI = \cancel\dfrac{6305}{8} \\ \\\longrightarrow \large \boxed{ \red{\tt CI =Rs. \: 788.12}}$

⠀

∴ Compound Interest will be Rs. 788.12

$\rule{300}{1}$

$\bf{ Given}\begin{cases}\sf{Principal = Rs.\:5000}\\\sf{Time = 3 \:Years}\\ \sf{Rate = 6\% \: p.a.}\\\sf{Simple\:Interest=?} \end{cases}$

• Calculation of Simple Interest :

$\longrightarrow \tt SI = \dfrac{P \times R \times T}{100} \\ \\\longrightarrow \tt SI = \dfrac{50\cancel{00} \times 6 \times 3}{1 \cancel{00}} \\ \\\longrightarrow \tt SI =50 \times 6 \times 3 \\ \\\longrightarrow \large \boxed{\red{\tt SI =Rs. \:900}}$

⠀

∴ Simple Interest will be Rs. 900

$\rule{300}{2}$

• D I F F E R E N C E ⠀I N ⠀I N T E R E S T :

↠ Difference = SI – CI

↠ Difference = Rs. (900 – 788.12)

↠ Difference = Rs. 111.88

⠀

∴ Difference of Interest will be Rs. 111.88

#answerwithquality #BAL

Answer 2

Compound Interest :-

Principal=₹5000

Time=3 years

Rate=5%

Compound Interest= Amount- Principal

Amount:-

$p \times { (1 + \frac{r}{100} )} ^ {t}$

$5000( {1 + \frac{5}{100}) }^{3}$

$5000 \times ( \frac{105}{100} ) ^{3}$

$5000 \times \frac{105 \times 105 \times 105}{100 \times 100 \times 100}$